For the system described by \[\mathop {\rm{X}}\limits^ \cdot \] = AX match List-I with List-II and select the correct answer.
| List-I (Matrix A) | List-II (Position of eigen values) |
| a. \[\left[ {\begin{array}{*{20}{c}} { - 1}&2\\ 0&{ - 2} \end{array}} \right]\] | 1. One eigen value at the origin |
| b. \[\left[ {\begin{array}{*{20}{c}} { - 1}&{ - 2}\\ { - 2}&{ - 4} \end{array}} \right]\] | 2. Both the eigen value in the LHP |
| c. \[\left[ {\begin{array}{*{20}{c}} 0&{ - 1}\\ 1&0 \end{array}} \right]\] | 3. Both the eigen values in RHP |
| d. \[\left[ {\begin{array}{*{20}{c}} 1&0\\ 2&4 \end{array}} \right]\] | 4. Both the eigen values on the imaginary axis |
A. a-2, b-1, c-3, d-4
B. a-2, b-1, c-4, d-3
C. a-1, b-2, c-4, d-3
D. a-1, b-2, c-3, d-4
Answer: Option B

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